% Copyright 2020 Makani Technologies LLC
%
% Licensed under the Apache License, Version 2.0 (the "License");
% you may not use this file except in compliance with the License.
% You may obtain a copy of the License at
%
%      http://www.apache.org/licenses/LICENSE-2.0
%
% Unless required by applicable law or agreed to in writing, software
% distributed under the License is distributed on an "AS IS" BASIS,
% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
% See the License for the specific language governing permissions and
% limitations under the License.

function [E_k] = kepler_anomaly(ecc, M_k)
% Compute the GPS Kepler anomaly.
tol = 1e-10;
E_k = M_k + ecc * sin(M_k) / (1 - sin(M_k + ecc) + sin(M_k));
for iter = 1:10
  Delta_E = (E_k - ecc * sin(E_k) - M_k) / (1 - ecc * cos(E_k));
  E_k = E_k - Delta_E;
  if abs(Delta_E) < tol
    break;
  end
end
